论文标题
在可比较的盒子尺寸上
On Comparable Box Dimension
论文作者
论文摘要
如果其中一个是另一个翻译的子集，则$ \ mathbb {r}^d $中的两个盒子是可比的。图$ g $的可比较框尺寸是最小整数$ d $，因此可以将$ g $表示为$ \ mathbb {r}^d $的可比轴对准框的接触图。我们表明，适当的次要封闭类具有可比较的框尺寸，并探索了该概念的进一步属性。
Two boxes in $\mathbb{R}^d$ are comparable if one of them is a subset of a translation of the other one. The comparable box dimension of a graph $G$ is the minimum integer $d$ such that $G$ can be represented as a touching graph of comparable axis-aligned boxes in $\mathbb{R}^d$. We show that proper minor-closed classes have bounded comparable box dimensions and explore further properties of this notion.
